Influence of optimal control on bifurcations of 3D axisymmetric buoyant flows
2009 - M.C. Navarro, H. Herrero
International Journal of Bifurcation and Chaos 19, 1279-1288, (2009)
Abtract
This paper shows the effects of optimal control techniques on pattern formation in a three-dimensional Rayleigh–Bénard problem with nonhomogeneous heating from below. In particular, we consider a cylindrical domain with a heating profile at the bottom localized around the origin. An axisymmetric basic state appears as soon a nonzero horizontal temperature gradient is imposed. The basic state may bifurcate to different solutions as spiral waves, stationary patterns, etc., depending on the vertical and lateral temperature gradients and on the shape of the heating function. An optimal control problem that determines the thermal boundary condition minimizing the enstrophy is proposed. The control boundary condition obtained changes the leading mode in the bifurcation and allows to eliminate the instabilities for some values of the parameters.